Document Zbl 0461.47012

Subnormal operators, Toeplitz operators and spectral inclusion. (English) Zbl 0461.47012

Trans. Am. Math. Soc. 263, 125-135 (1981).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0461.47012

MSC:

47B20	Subnormal operators, hyponormal operators, etc.
47B35	Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A10	Spectrum, resolvent
47A20	Dilations, extensions, compressions of linear operators

Keywords:

subnormal operator; spectral inclusion theorems; reducing essential spectrum; extremely noncompact operator

Citations:

Zbl 0049.090; Zbl 0035.359

Cite Review PDF

Full Text: DOI

References:

[1]	M. B. Abrahamse and R. G. Douglas, A class of subnormal operators related to multiply-connected domains, Advances in Math. 19 (1976), no. 1, 106 – 148. · Zbl 0321.47019 · doi:10.1016/0001-8708(76)90023-2
[2]	J. W. Bunce and J. A. Deddens, On the normal spectrum of a subnormal operator, Proc. Amer. Math. Soc. 63 (1977), no. 1, 107 – 110. · Zbl 0351.47022
[3]	L. A. Coburn, Weyl’s theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285 – 288. · Zbl 0173.42904
[4]	Ronald G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York-London, 1972. Pure and Applied Mathematics, Vol. 49. · Zbl 0247.47001
[5]	R. G. Douglas and Carl Pearcy, Spectral theory of generalized Toeplitz operators, Trans. Amer. Math. Soc. 115 (1965), 433 – 444. · Zbl 0151.19604
[6]	P. A. Fillmore, J. G. Stampfli, and J. P. Williams, On the essential numerical range, the essential spectrum, and a problem of Halmos, Acta Sci. Math. (Szeged) 33 (1972), 179 – 192. · Zbl 0246.47006
[7]	Richard Frankfurt, Subnormal weighted shifts and related function spaces, J. Math. Anal. Appl. 52 (1975), no. 3, 471 – 489. · Zbl 0319.47024 · doi:10.1016/0022-247X(75)90074-8
[8]	Paul R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, AMS Chelsea Publishing, Providence, RI, 1998. Reprint of the second (1957) edition. · Zbl 0962.46013
[9]	Paul R. Halmos, Spectra and spectral manifolds, Ann. Soc. Polon. Math. 25 (1952), 43 – 49 (1953). · Zbl 0049.09001
[10]	Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. · Zbl 0144.38704
[11]	P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887 – 933. · Zbl 0204.15001
[12]	Philip Hartman and Aurel Wintner, On the spectra of Toeplitz’s matrices, Amer. J. Math. 72 (1950), 359 – 366. · Zbl 0035.35903 · doi:10.2307/2372039
[13]	Robert F. Olin, Functional relationships between a subnormal operator and its minimal normal extension, Pacific J. Math. 63 (1976), no. 1, 221 – 229. · Zbl 0323.47018
[14]	Carl M. Pearcy, Some recent developments in operator theory, American Mathematical Society, Providence, R.I., 1978. Regional Conference Series in Mathematics, No. 36. · Zbl 0444.47001
[15]	Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Amer. Math. Soc., Providence, R.I., 1974, pp. 49 – 128. Math. Surveys, No. 13. · Zbl 0303.47021

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.